The number of integral values of $k$ for which the equation $x^2 - 2(3k - 1)x + 8k^2 - 7 > 0$ holds for all real $x$ is:
Step-by-Step Solution
Key Concept: For the quadratic (leading coeff. positive) to be always positive, the discriminant must be $< 0$. Compute $D < 0$ to get a quadratic inequality in $k$, then count integers inside that range.
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Correct Answer: (2)